MULTIFRACTAL PROPERTIES OF R90 CELLULAR AUTOMATON WITH MEMORY

2004 ◽  
Vol 15 (10) ◽  
pp. 1461-1470 ◽  
Author(s):  
JUAN R. SÁNCHEZ ◽  
RAMÓN ALONSO-SANZ
Keyword(s):  
Cellular Automata ◽  
Complex Behavior ◽  
Time Step ◽  
One Dimensional ◽  
Dynamical Characteristics ◽  
Historic Memory ◽  
A Cell ◽  
Update Rules ◽  
With Memory ◽  
Standard Framework

Standard Cellular Automata (CA) are ahistoric (memoryless Markov process), i.e., the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article considers the fractal and multifractal properties of an extension to the standard framework of CA implemented by the inclusion of memory capabilities. Thus, in CA with memory, while the update rules of the CA remain unaltered, historic memory of all past iterations is retained by featuring each cell by a summary of all its past states. A study is made of the effect of historic memory on the multifractal dynamical characteristics of one-dimensional cellular automata operating under one of the most studied rules, rule 90, which is well known to display a rich complex behavior.

ONE-DIMENSIONAL r=2 CELLULAR AUTOMATA WITH MEMORY

2004 ◽  
Vol 14 (09) ◽  
pp. 3217-3248 ◽  
Author(s):  
RAMÓN ALONSO-SANZ
Keyword(s):  
Cellular Automata ◽  
Time Step ◽  
One Dimensional ◽  
The Past ◽  
A Cell ◽  
Factor Α ◽  
Update Rules ◽  
With Memory ◽  
Standard Framework ◽  
Dimensional Range

Standard Cellular Automata (CA) are ahistoric (memoryless): i.e. the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article introduces an extension to the standard framework of CA by considering automata implementing memory capabilities. While the update rules of the CA remains the same, each site remembers a weighted mean of all its past states, with a decreasing weight of states farther in the past. The historic weighting is defined by a geometric series of coefficients based on a memory factor (α). This paper considers the time evolution of one-dimensional range-two CA with memory.

ONE-DIMENSIONAL CELLULAR AUTOMATA WITH MEMORY: PATTERNS FROM A SINGLE SITE SEED

2002 ◽  
Vol 12 (01) ◽  
pp. 205-226 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
MARGARITA MARTÍN
Keyword(s):  
Cellular Automata ◽  
Weighted Mean ◽  
Time Step ◽  
Memory Factor ◽  
One Dimensional ◽  
A Cell ◽  
Factor Α ◽  
Update Rules ◽  
With Memory ◽  
Standard Framework

Standard Cellular Automata (CA) are ahistoric (memoryless): i.e. the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article introduces an extension to the standard framework of CA by considering automata implementing memory capabilities. While the update rules of the CA remain the same, each site remembers a weighted mean of all its past states. The historic weighting is defined by a geometric series of coefficients based on a memory factor (α). The time evolution of one-dimensional CA with memory starting with a single live cell is studied. It is found that for α ≤ 0.5, the evolution corresponds to the standard (nonweighted) one, while for α > 0.5, there is a gradual decrease in the width of the evolving pattern, apart from discontinuities which sometimes may occur for certain rules and α values.

CELLULAR AUTOMATA WITH ACCUMULATIVE MEMORY: LEGAL RULES STARTING FROM A SINGLE SITE SEED

2003 ◽  
Vol 14 (05) ◽  
pp. 695-719 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
MARGARITA MARTÍN
Keyword(s):  
Cellular Automata ◽  
Forgetting Factor ◽  
Weighted Mean ◽  
Time Step ◽  
One Dimensional ◽  
Legal Rules ◽  
The Past ◽  
A Cell ◽  
Update Rules ◽  
Standard Framework

Standard Cellular Automata (CA) are ahistoric (memoryless), i.e., the new state of a cell depends only on the neighborhood configuration at the preceding time step. This article introduces an extension of the standard framework of CA by considering automata implementing memory capabilities. While the update rules of the CA remains the same, each site remembers a weighted mean of all its past states, with a decreasing weight of states farther back in the past. The historic weighting is defined by a potential series of coefficients, tk, k acting as a forgetting factor. This paper considers the time evolution of one-dimensional, legal CA rules with accumulative memory.

TWO-DIMENSIONAL CELLULAR AUTOMATA WITH MEMORY: PATTERNS STARTING WITH A SINGLE SITE SEED

2002 ◽  
Vol 13 (01) ◽  
pp. 49-65 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
MARGARITA MARTÍN
Keyword(s):  
Cellular Automata ◽  
Single Site ◽  
Two Dimensional ◽  
Time Step ◽  
A Cell ◽  
With Memory

Standard Cellular Automata (CA) are ahistoric (memoryless), i.e., the new state of a cell depends on its neighborhood configuration only at the preceding time step. The effect of keeping ahistoric memory of all past iterations in two-dimensional CA, featuring each cell by its most frequent state is analyzed in this work.

Phase Transition in Elementary Cellular Automata with Memory

2014 ◽  
Vol 24 (09) ◽  
pp. 1450116 ◽  
Author(s):  
Shigeru Ninagawa ◽  
Andrew Adamatzky ◽  
Ramón Alonso-Sanz
Keyword(s):  
Cellular Automata ◽  
State Transition ◽  
Time Interval ◽  
Complex Behavior ◽  
Weighted Function ◽  
Transition Functions ◽  
Elementary Cellular Automata ◽  
Computational Universality ◽  
With Memory ◽  
Time Automaton

We study elementary cellular automata with memory. The memory is a weighted function averaged over cell states in a time interval, with a varying factor which determines how strongly a cell's previous states contribute to the cell's present state. We classify selected cell-state transition functions based on Lempel–Ziv compressibility of space-time automaton configurations generated by these functions and the spectral analysis of their transitory behavior. We focus on rules 18, 22, and 54 because they exhibit the most intriguing behavior, including computational universality. We show that a complex behavior is observed near the nonmonotonous transition to null behavior (rules 18 and 54) or during the monotonic transition from chaotic to periodic behavior (rule 22).

BOOLEAN NETWORKS WITH MEMORY

2008 ◽  
Vol 18 (12) ◽  
pp. 3799-3814 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
LARRY BULL
Keyword(s):  
Boolean Networks ◽  
Time Step ◽  
Different Types ◽  
A Cell ◽  
With Memory ◽  
In Cells

In standard Boolean Networks (BN) the new state of a cell depends upon the neighborhood configuration only at the preceding time step. The effect of implementing memory of different types in cells of BN with different degrees of random rewiring is studied in this article.

Pseudorandom Number Generators Based on Asynchronous Cellular Automata and Cellular Automata With Inhomogeneous Cells

2017 ◽  
pp. 127-138
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Local State ◽  
Active Cell ◽  
State Function ◽  
Local Function ◽  
Time Step ◽  
Random Number Generators ◽  
Asynchronous Cellular Automata ◽  
A Cell

The sixth chapter deals with the construction of pseudo-random number generators based on a combination of two cellular automata, which were considered in the previous chapters. The generator is constructed based on two cellular automata. The first cellular automaton controls the location of the active cell on the second cellular automaton, which realizes the local state function for each cell. The active cell on the second cellular automaton is the main cell and from its output bits of the bit sequence are formed at the output of the generator. As the first cellular automaton, an asynchronous cellular automaton is used in this chapter, and a synchronous cellular automaton is used as the second cellular automaton. In this case, the active cell of the second cellular automaton realizes another local function at each time step and is inhomogeneous. The algorithm for the work of a cell of a combined cellular automaton for implementing a generator and its hardware implementation are presented.

scholarly journals Detecting synchronization in spatially extended discrete systems by complexity measurements

2005 ◽  
Vol 2005 (3) ◽  
pp. 337-342 ◽  
Author(s):  
Juan R. Sánchez ◽  
Ricardo López-Ruiz
Keyword(s):  
Cellular Automata ◽  
Discrete Systems ◽  
Complex Behavior ◽  
Singular Behavior ◽  
One Dimensional ◽  
Statistical Complexity ◽  
Spatially Extended ◽  
The Difference

The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns generated by the difference automaton. This singular behavior is verified to be present in several CA rules displaying complex behavior.

Three-state one-dimensional cellular automata with memory

2004 ◽  
Vol 21 (4) ◽  
pp. 809-834 ◽  
Author(s):  
Ramón Alonso-Sanz ◽  
Margarita Martı́n
Keyword(s):  
Cellular Automata ◽  
One Dimensional ◽  
With Memory

RANDOM NUMBER GENERATION BY CELLULAR AUTOMATA WITH MEMORY

2008 ◽  
Vol 19 (02) ◽  
pp. 351-367 ◽  
Author(s):  
RAMÓN ALONSO-SANZ ◽  
LARRY BULL
Keyword(s):  
Cellular Automata ◽  
Random Number ◽  
Random Number Generation ◽  
Random Number Generators ◽  
Potential Value ◽  
Number Generation ◽  
Elementary Cellular Automata ◽  
With Memory ◽  
Standard Framework

This paper considers an extension to the standard framework of cellular automata which implements memory capabilities by featuring cells by elementary rules of its last three states. A study is made of the potential value of elementary cellular automata with elementary memory rules as random number generators.

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